In a botanical study of Mirabilis jalapa (four o'clock flower), flower color exhibits incomplete dominance. A cross between two pink-flowered plants is expected to produce offspring with red, pink, and white flowers in a phenotypic ratio of 1 red : 2 pink : 1 white.
A researcher cultivated 40 offspring plants from such a cross and analyzed the resulting distribution of flower colors.
The researcher performed a chi-squared (χ2\chi^2χ2) test on the phenotypes of the actual 40 offspring. Part of the calculation is shown in the table below.
| Phenotypes | Observed number (OOO) | Expected number (EEE) | O−EO-EO−E | (O−E)2(O-E)^2(O−E)2 | (O−E)2E\frac{(O-E)^2}{E}E(O−E)2 |
|---|---|---|---|---|---|
| Red flowers | -2.0 | 4.0 | 0.40 | ||
| Pink flowers | 3.0 | 9.0 | 0.45 | ||
| White flowers | -1.0 | 1.0 | 0.10 | ||
| χ2=\chi^2 =χ2= | 0.95 |
Complete the table by finding the value of the observed (OOO) and expected (EEE) numbers for each phenotype.
Using the portion of the χ2\chi^2χ2 critical values table below, identify the critical value for this test at the 5%5\%5% significance level (p=0.05p = 0.05p=0.05).
| Degrees of freedom (ν\nuν) | 10%10\%10% level (p=0.10p=0.10p=0.10) | 5%5\%5% level (p=0.05p=0.05p=0.05) | 1%1\%1% level (p=0.01p=0.01p=0.01) |
|---|---|---|---|
| 1 | 2.706 | 3.841 | 6.635 |
| 2 | 4.605 | 5.991 | 9.210 |
| 3 | 6.251 | 7.815 | 11.340 |
State whether the researcher should accept or reject the null hypothesis (that there is no significant difference between the observed and expected phenotypic ratios), and justify your answer using the calculated χ2\chi^2χ2 value and the critical value.
